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Molecular Orbital Theory is a chemical bonding theory that states that individual atoms combine to form molecular orbitals. In molecular orbital theory or MOT, the electrons in a molecule are not assigned to individual chemical bonds between the atoms. Rather, they are treated as moving under the influence of the atomic nuclei in the entire molecule.
- The theory was developed by F. Hund and R. S. Mulliken at the beginning of the 20th century.
- It aimed to describe the structure and properties of different molecules that can’t be explained by the valence bond theory.
- These molecules involve a form of resonance that implies the bond is neither single nor double but a hybrid.
- The orbitals described by molecular orbital theory reflect the geometries of the molecules to which it is applied.
- The molecular orbital theory revolutionized the study of chemical bonding by approximating the bonded electron states.
- It helps in predicting the shape of pre-bonding atomic orbitals and post-bonding molecular orbitals.
What is Molecular Orbital Theory?
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Molecular Orbital Theory states that the electrons of an atom, associated with several nuclei, are present in multiple atomic orbitals. It uses quantum mechanics to describe the electronic structure of molecules.
- Derived from quantum mechanical equations, it predicts the probable locations of electrons in atoms or molecules.
- According to this theory, atoms combine to create molecular orbitals, and electrons reside in different atomic orbitals, associated with distinct nuclei.
This means that electrons can be located anywhere within a molecule. Thus, in chemistry, the complete explanation of molecular orbital theory is given as follows:
| “Molecular Orbital Theory or MOT helps us understand how electrons exist within a molecule. The filling of molecular orbitals follows the increasing order of orbital energy.” |
Molecular Orbital Theory
Postulates of Molecular Orbital Theory
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In chemistry, there are five postulates of Molecular Orbital Theory which are discussed below:
- The total number of molecular orbitals formed is equal to the total number of atomic orbitals brought by the atomics that combine.
- The electrons in the molecular orbital are filled in the increasing order of orbital energy (from orbital having lower energy to orbital having higher energy).
- Molecular Orbital Theory describes three types of orbital based on the pattern of electron bonding. These are –
- Bonding Molecular Orbital
- Non-bonding Molecular Orbital
- Anti-bonding Molecular Orbital
- Out of these, antibonding molecular orbitals always have higher energy than the parent orbitals.
- However, molecular orbitals always have lower energy than parent orbitals.
Rules of Molecular Orbital Theory
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Molecular Orbitals
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Molecular orbitals are the mathematical functions that explain the wave nature of electrons in a given molecule. The space in a molecule in which the probability of finding an electron is maximum can be calculated using the molecular orbital function.
- These orbitals can be constructed via the combination of hybridized orbitals and atomic orbitals.
- Molecular orbitals can be used as a model in the molecular orbital theory to demonstrate the bonding of molecules.
- There are three types of molecular orbitals – Bonding Molecular Orbital, Anti-bonding molecular orbital, and Non-bonding molecular orbital.
Molecular Orbitals of the Second Energy Level
For example, the molecular orbital diagram of O2 can be represented as follows –
- Oxygen has an electron configuration of 1s²2s²2p⁴, contributing a total of twelve valence electrons in O2 (six from each oxygen atom).
- The molecular orbital diagram reveals the presence of two electrons in antibonding orbitals.
- Each electron occupies a separate π* orbital, following Hund's Rule to minimize electron-electron repulsion.
- The bond energy of O2 is 498 kJ/mole, notably lower than the 945 kJ bond energy of N2.
- This difference is attributed to oxygen having two electrons in antibonding orbitals, while nitrogen has only one.
- Dioxygen (O2) exhibits paramagnetism due to the presence of two unpaired electrons in its molecular orbitals.
- This property is demonstrated by the liquid O2 being attracted to the poles of a strong permanent magnet.
- Removing an electron to form O2+ increases the ratio of bonding to antibonding electrons, resulting in a more stable molecule.
- Conversely, adding an electron to O2 weakens the bond, as seen in the lower bond energy of O2–.
- These dioxygen ions are highly reactive and observed only in the gas phase.
The observed stability changes in O2+, O2, and O2– align with the expectations from the molecular orbital model, validating its accuracy in predicting bond energies and stability.
Molecular Diagram of O2
Formation of Molecular Orbitals
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According to wave mechanics, the atomic orbitals can be expressed by wave functions (ψ’s).
- The wave functions also represent the amplitude of the electron waves.
- These can be obtained from the Schrodinger wave equation.
- However, the Schrodinger wave equation cannot be solved for any system containing more than one electron.
- Therefore, it is difficult to obtain molecular orbitals which are one-electron wave functions for molecules from the solution of the Schrodinger wave equation.
- To overcome this problem, the Linear Combination of Atomic Orbitals (LCAO) has been adopted.
How are Molecular Orbitals Formed?
Molecular orbitals form when atomic orbitals combine in a molecule. Taking H2 as an example, the two 1s atomic orbitals combine by adding, creating a molecular orbital. Another orbital is formed by subtracting one from the other.
- Bonding Molecular Orbital (σ): Electrons spend most time between nuclei, stabilizing the molecule.
- Antibonding Molecular Orbital (σ):* Electrons spend less time between nuclei, making the molecule less stable.
| The bonding orbital is formed by the addition of the orbitals. The antibonding orbital is formed by subtracting the orbitals. |
For H2, placing electrons in the bonding orbital makes the molecule more stable. Therefore, the H2 molecule is more stable than isolated atoms. This demonstrates the power of molecular orbital theory in predicting stability. The bonding and antibonding orbitals diagram of hydrogen is given below:
Bond OrderBond order is the number of bonds between two atoms. Lewis structures, an important part of the valence-bond model, help calculate bond orders. Bond Order = \(Bonding\ electrons - Antibonding\ electrons \over 2\) Example: Oxygen has a bond order of two. For molecules with multiple structures (e.g., sulfur dioxide), its bond order is an average. Sulfur dioxide has a bond order of 1.5, considering its different Lewis structures.
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Linear Combination of Atomic Orbitals (LCAO)
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Molecular orbitals can be calculated by quantum chemistry technique called Linear Combination of Atomic Orbitals (LCAO). These LCAOs are useful to estimate the orbital formation in atom bonding within molecules. The application of LCAO can also be seen in explaining the wave-like motion of electrons in an atom.
- The Schrodinger equation used to describe electron behaviour in molecular orbitals can be written similarly to atomic orbitals.
- It is an approximate method which is useful for representation of molecular orbitals.
- LCAO is a superimposition method where constructive interference of 2 atomic wave functions produces bonding molecular orbital.
- Destructive interference produces a non-bonding molecular orbital.
Conditions for Linear Combination of Atomic Orbitals
The three main conditions for linear combination of atomic orbitals (LCAO) to be suitable as approximate molecular orbitals are as given below:
Same Energy of Combining Orbitals
- The combining atomic orbitals must have the same or approximately the same energy.
- This means that the 2p orbital of an atom can combine with another 2p orbital of another atom but 1s and 2p cannot combine as they have energy differences.
Same Symmetry about Molecular Axis
- The combining atoms should have the same symmetry around the molecular axis for proper combination.
- For e.g. all the sub-orbitals of 2p have the same energy but still, the 2pz orbital of an atom can only combine with a 2pz orbital of another atom.
- It cannot combine with 2px and 2py orbital because they have a different axis of symmetry.
Proper Overlapping between Atomic Orbitals
- The two atomic orbitals will combine to form a molecular orbital only if the overlap is proper.
- The greater the extent of overlap of orbitals, the greater will be the nuclear density between the nuclei of the two atoms.
- For the formation of a proper molecular orbital, proper orientation and energy are required.
- For proper energy, two atomic orbitals should have the same energy and for proper orientation, the atomic orbitals should have proper overlap with the same molecular axis of symmetry.
Molecular Orbital Model: Why some Molecules do Not Exist?The molecular orbital model provides valuable insights into the stability and existence of molecules. One example is the case of helium molecules (He2).
The molecular orbital model, by revealing the lack of stability and energy advantage in the formation of He2 molecules, underscores the role of valence-shell interactions and highlights the principle that core orbitals play a negligible role in determining molecular stability. Thus, certain molecules, such as He2, do not exist under normal conditions. |
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Types of Molecular Orbitals
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According to Molecular Orbital Theory, there are three types of Molecular Orbitals. These Molecular Orbitals are as follows:
- Bonding Molecular Orbital
- Anti-bonding molecular orbital
- Non-bonding molecular orbital
Bonding Molecular Orbital
According to Molecular Orbital Theory, the molecular orbital which is formed by the addition of overlapping of atomic orbital is called Bonding Molecular Orbital.
Characteristics of Bonding Molecular Orbital
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Anti-bonding Molecular Orbital
The molecular orbital which is formed by the subtraction of overlapping atomic orbital is called Bonding Molecular Orbital.
Characteristics of Anti-bonding Molecular Orbital
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Types of Molecular Orbitals
Non-Bonding Molecular Orbital
According to Molecular Orbital Theory, a lack of symmetry between the compatibility of two atomic orbitals will result in a nonbonding molecular orbital. There is no force of attraction and repulsion exists to form wave function between the atoms.
Characteristics of Nonbonding Molecular Orbital
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Difference between Bonding and Antibonding Molecular Orbitals
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The difference between bonding and antibonding molecular orbitals of the MOT Theory are as follows –
| Bonding Molecular Orbitals | Anti-Bonding Molecular Orbitals |
|---|---|
| Formed by the additive effect of atomic orbitals. | Formed by the subtractive effect of atomic orbitals. |
| The probability of finding electrons is higher in the case of bonding molecular orbitals | The probability of finding electrons is less in antibonding molecular orbitals. |
| Formed through the combination of + and + and – with – part of the electron waves | Formed by the overlap or combination of + with the – part. |
| Electron density in the internuclear region – high – nuclei shielded from each other – less repulsion. | Electron density in the internuclear region – very low – nuclei directly exposed to each other – less shielded. |
| These molecular orbitals are represented by σ, π, δ. | These molecular orbitals are represented by σ∗ , π∗, δ∗. |
Importance of Molecular Orbital Theory in Chemistry
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The needs for Molecular Orbital Theory are as follows –
- Molecular Orbital Theory addresses molecules with resonance, where certain molecules exhibit two or more equivalent bonds with bond orders between single and double bonds.
- Valence bond theory falls short in explaining the unique bonding characteristics observed in certain molecules.
- Molecular Orbital Theory is preferred as it accurately reflects the geometry of molecules.
- Molecular Orbital Theory has demonstrated greater applicability in understanding complex molecular structures.
These needs highlight the shortcomings of the valence bond theory and emphasize the ability of Molecular Orbital Theory to address and explain these limitations.
Read More: NCERT Solutions for Class 11 Chemistry Chemical Bonding and Molecular Structure
Features of Molecular Orbital Theory
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According to Molecular Orbital Theory, the orbitals are filled as per the following rules/principles:
- Aufbau’s principle: Molecular orbitals are filled in the increasing order of energy levels.
- Pauli’s exclusion principle: No two electrons can have the same set of four quantum numbers in an atom or a molecule.
- Hund’s rule of maximum multiplicity: Pairing of electrons doesn’t take place until all the atomic or molecular orbitals are singly occupied.
Valence Bond Theory vs Molecular Orbital Theory
Atomic orbitals explain how valence electrons form bonds. This is often associated with valence-bond theory.
- Valence-bond theory can not explain molecules with two equivalent bonds with a bond order between that of a single bond and a double bond.
- It suggests that the molecules are mixtures or hybrid structures but fall short.
- This problem can be overcome by using molecular orbital theory – a model based on molecular orbitals.
- It is more efficient than valence bond theory as the orbitals reflect the geometry of the molecule to which they are applied.
- However, it is a difficult model to visualize.
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Things to Remember
- Molecular Orbital Theory describes the electronic structure of molecules to calculate the movement and sharing of electrons.
- Atoms combine to form molecular orbitals, governed by principles such as similar energy levels and symmetry.
- According to MOT, total number of molecular orbitals equals the total number of atomic orbitals.
- Electrons fill these orbitals in increasing energy order.
- Molecular orbitals come in three types: Bonding (σ), Antibonding (σ*), and Non-bonding.
- Molecular orbitals are formed through constructive interference leading to bonding and destructive interference leading to antibonding.
- Bonding Molecular Orbitals (MOs) are characterized by lower energy, higher stability, and electron attraction.
- Antibonding MOs have higher energy and electron repulsion.
- Molecular orbitals are filled according to principles like Aufbau, Pauli exclusion, and Hund's rule.
- The theory also reflects the geometries of molecules, contributing to predicting their behaviour.
Read More: Isotopes and Isobars
Previous Years’ Questions
Questions on Molecular Orbital Theory Class 11
Ques. Using molecular orbital theory, compare the bond energy and magnetic character of O2+ and O2–. (2 Marks)
Ans. O2+(15): \(\sigma\)1s2 \(\sigma\)*1s2 \(\sigma\)2s2 \(\sigma\)*2s2 \(\sigma\)2p2z \(\pi\)2px2 = \(\pi\)2py2 \(\pi\)*2px1
B.O. = ½ (10 – 5) = 2.5
O2-(17): \(\sigma\)1s2 \(\sigma\)*1s2 \(\sigma\)2s2 \(\sigma\)*2s2 \(\sigma\)2p2z \(\pi\)2px2 = \(\pi\)2py2 \(\pi\)*2px2 = \(\pi\)*2py1
B.O. = ½ (10 – 7) = 1.5
Bond Energy of O2+ > O2-
Both are paramagnetic due to the presence of unpaired electrons.
Ques. Draw the molecular orbital diagram of dihelium. (5 marks)
Ans. The dihelium positive ion (He₂⁺) consists of two helium nuclei and three electrons.
- While stable, it is not as stable as dihydrogen (H₂), requiring 301 kJ/mole to break apart.
- Two electrons occupy the bonding orbital, but the third electron enters the higher sigma antibonding orbital.
- The presence of an electron in the antibonding orbital introduces a repulsive component, partially countering the attractive effect of the filled bonding orbital
- The bond energy of dihelium is only 0.084 kJ/mol.
- Insufficient energy to withstand thermal motion at ordinary temperatures causes rapid dissociation.
Ques. Give an example of a molecular orbital diagram of atomic molecules containing second-row atoms. (3 marks)
Ans. Lithium (Li) has an electronic configuration of 1s²2s¹.
- When lithium bonds with itself to form Li2, the focus shifts to the σ bonding and antibonding orbitals, leaving aside the 1s atomic orbitals.
- There are not enough electrons to populate the antibonding orbital fully.
- The attractive forces outweigh the repulsive forces due to the incomplete population of the antibonding orbital, resulting in the formation of a stable molecule.
- The bond energy of dilithium is measured at 110 kJ/mole.
- The bond energy of dilithium (Li2) is significantly less than half of the bond energy of dihydrogen (H2), which also has two electrons in a bonding orbital.
- A general rule is established that the larger the parent atom, the less stable the corresponding diatomic molecule.
- This is attributed to the increased distance of the valence orbitals from the nucleus in larger atoms.
Thus, dilithium (Li2) exemplifies stability in a molecular context, with considerations of electron population in bonding and antibonding orbitals influencing the overall stability of the diatomic molecule.
Ques. The energy of σ2pz: molecular orbital is greater than 2px and 2pv molecular orbitals in nitrogen molecule. Write the complete sequence of energy levels in the increasing order of energy in the molecule. Compare the relative stability and the magnetic behaviour of the following species: N2, N2–, N2+, N22+ (2 Marks)
Ans. The sequence of Energy Levels can be given as:
Stability Order: N2 > N2– > N2+ > N22+
N2– has more bonding electrons than N22+
Ques. (a) Define antibonding molecular orbital.
(b) Out of bonding and antibonding molecular orbitals, which one has lower energy and which one has higher stability? (2 Marks)
Ans. (a) The molecular orbital formed by the subtractive effect of the electron waves of the combining atomic orbitals, is called an antibonding molecular orbital.
(b) Bonding molecular orbital has lower energy and higher stability.
Ques. What is Bond Order? (2 Marks)
Ans. The difference between the number of electrons present in bonding and antibonding orbitals results in bond order. The formula of bond order is B.O = ½ [Nb – Na]. Bond order can either be positive, negative, whole number or fraction.
Ques. What is Bond length? (2 Marks)
Ans. The length between the bonds is called bond length. Bond length is always inversely proportional to the Bond order. The greater the bond order, smaller will be the bond length and vice versa.
Ques. How to detect whether a molecule is paramagnetic or diamagnetic? (2 Marks)
Ans. If the molecular orbitals of a molecule have one or more unpaired electrons, it is paramagnetic. On the other hand, if every molecular orbital has paired electrons, it is diamagnetic in nature.
Ques. What are the different types of hydrogen bonding? (2 Marks)
Ans. Hydrogen bonding can be classified into two types such as Intermolecular Hydrogen Bonding and Intramolecular Hydrogen Bonding.
- Intermolecular Hydrogen Bonding: Intermolecular hydrogen bonding is the bond that is formed between two same or different atoms.
- Intramolecular Hydrogen Bonding: In Intramolecular Hydrogen Bonding, hydrogen is bonded to two highly electronegative atoms of Flourine, Oxygen and Nitrogen.
Ques. Write the Principles that are followed by the Molecular Orbital Theory. (3 Marks)
Ans. According to Molecular Orbital Theory, the orbitals are filled by the following rules/principles :
- Aufbau’s principle: The filling of molecular orbital takes place according to the increasing order of energy levels.
- Pauli’s exclusion principle: In an atom or a molecule, no two electrons can have the same set of four quantum numbers.
- Hund’s rule of maximum multiplicity: Pairing of electrons doesn’t take place until all the atomic or molecular orbitals are singly occupied.
Ques. Write the important conditions required for the linear combination of atomic orbitals to form molecular orbitals. (3 Marks)
Ans. The important conditions that are required for the linear combination of atomic orbitals to form molecular orbitals are:
- The combining atomic orbitals should have comparable energies.
For example, 1s orbital of one atom can combine with 1s atomic orbital of another atom, 2s can combine with 2s. - The combining atomic orbitals must have proper symmetry. So that they can overlap easily.
- The extent of overlapping should be large.
Ques. Use the molecular orbital energy level diagram to show that N2 would be expected to have a triple bond, F2 a single bond, and Ne2 no bond. (5 Marks)
Ans. N2 Molecule = Electronic Configuration of N-atom (Z=7) is 1s22s22px12py12pz1.
Total number of electrons present in N2 molecule is 14, 7 from each N-atom.
The electronic configuration of N2 molecule will be σ1s2 σ*1s2 σ2s2 σ*2s2 π2px1 π2py1 σ2pz1.
Bond Order of N2 molecule = 1/2(10-4) = 3 (Triple Bond)
F2 Molecule = Electronic Configuration of F-atom (Z=9) is 1s22s22px22py22pz1.
Total number of electrons present in F2 molecule is 18, 9 from each F-atom.
The electronic configuration of F2 molecule will be σ1s2 σ*1s2 σ2s2 σ*2s2 σ2pz2 π2px2 π2py2 π*2px2 π*2py2.
Bond Order of F2 molecule = 1/2(10-8) = 1 (Single Bond)
Ne2 Molecule = Total number of electrons present in Ne2 molecule is 20, 10 from each Ne-atom.
The electronic configuration of Ne2 molecule will be σ1s2 σ*1s2 σ2s2 σ*2s2 σ2pz2 π2px2 π2py2 π*2px2 π*2py2 σ*2pz2 .
Bond Order of F2 molecule = 1/2(10-10) = 0 (No Bond)
Ques. Draw the molecular orbital diagram of O2. (3 Marks)
Ans. The molecular orbital diagram of O2 is as given below:
Molecular Diagram of O2
Ques. What is the relationship between bond order and bond length? (2 Marks)
Ans. The bond length is the distance between two atoms in a given molecule. The bond order, on the other hand, depends on the bond length between two atoms in a molecule. Therefore, as the bond length increases the bond order decreases and vice-versa.
Ques. What is the Hund’s Rule? (2 Marks)
Ans. Hund’s rule states that in any two molecular orbitals of the same energy, the pairing of electrons occurs when each of the orbital having the same energy consist of one electron.
Ques. How is stability related to energy? (2 Marks)
Ans. As the stability increases, the energy of the substance decreases. The higher is the energy, the less stable is the molecule. Hence, we can say stability is inverse proportional to the energy.
Ques. How are the shapes of molecular orbitals determined? (1 Mark)
Ans. The shapes of the molecular orbitals are determined by the shapes of the combining atomic orbitals.
Ques. Why the bond order of N2 is greater than N2+ but the bond order of O2 is less than that of O2+? (2 Marks)
Ans. When N2 transforms into N2+, the electron is removed from the bonding molecular orbital whereas when O2 changes to O2+, the electron is removed from the antibonding molecular orbital. This is why the bond order of N2 is more than N2+ whereas the bond order of O2 is less than that of O2+.
Ques. Two p-orbitals from an atom and two p-orbitals from another atom are combined together to form molecular orbitals. How many molecular orbitals will be formed through this combination? Explain. (2 Marks)
Ans. Four molecular orbitals are formed by combining two p-orbitals from one atom and the two p-orbitals from another atom. Of these four molecular orbitals, two are bonding molecular orbitals and the other two are antibonding molecular orbitals.
Ques. What is the electronic configuration of atom Au? (1 Mark)
Ans. The electronic configuration of gold is [Xe]4f145d106s1
Ques. What is the relationship between bond order and the dissociation energy of a molecule? (1 Mark)
Ans. The dissociation energy of a molecule is directly proportional to its bond order.
Ques. Explain why an atomic orbital is monocentric whereas a molecular orbital is polycentric? (2 Marks)
Ans. An atomic orbital is under the influence of a nucleus while a molecular orbital is under the influence of two or more nuclei depending on the number of atoms in the molecule.
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